Out of 1100 discs tested 13 are defective. Estimate the number of defective discs in a batch of 41000
A $6,300.00 principal earns 6% interest, compounded annually. After 3 years, what is the balance in the account?
One of the parking lot lights at a hospital has a motion detector on it, and the equation (x+10)2+(y−8)2=16 describes the boundary within which motion can be sensed.
What is the greatest distance, in feet, a person could be from the parking lot light and be detected?
Triangle ABC is translated on the coordinate plane below to create triangle A'B'C':
If parallelogram EFGH is translated according to the same rule that translated triangle ABC, what is the ordered pair of point H'?
The new coordinates of Point H' will be (6, -5) after the translation.
Triangle ABC is translated on the coordinate plane below to create triangle A'B'C':
If parallelogram EFGH is translated according to the same rule that translated triangle ABC.
How to find the point after translation?In the triangle, point A is moved 5 units to the right side and down 6 units.
If we count the same amount of space right side and down from point H, we will end up on a point (6, -5).
Therefore, The new coordinates of Point H' will be (6, -5) after the translation.
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Russ is constructing the inscribed circle for △ABC . He has already used his compass and straightedge to complete the part of the construction shown in the figure.
What could be his next step?
A)Use the straightedge to draw a line through point N that intersects BC¯¯¯¯¯ .
B) Use the straightedge to draw the line through points M and P.
C) Place the point of the compass on point C and draw an arc that intersects AC¯¯¯¯¯ and BC¯¯¯¯¯ .
D)Place the point of the compass on point N and draw an arc that intersects AB¯¯¯¯¯ and BC¯¯¯¯¯ .
Answer: The answer is (C) Place the point of the compass on point C and draw an arc that intersects AC and BC.
Step-by-step explanation: Given that Russ is constructing the inscribed circle for △ABC and he has already used his compass and straightedge to complete the part of the construction shown in the given figure. We are to find his next step.
Since Russ has already constructed the angle bisector of ∠B, so next he shoul construct the angle bisector of either ∠A or ∠C. Since the steps for constructing angle bisector of ∠A are not in the options, so he should go with ∠C. For that, he must place the point of the compass on the point C and draw an arc that intersects AC and BC.
Thus, (C) is the correct option.
angle measure represented by 4.5 rotations counterclockwise
In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 7 in?
Enter your answer in the box.
The length of the hypotenuse is 14in
SOH CAH TOA identityGiven a 30-60-90 triangle where:
Length of the shorter leg = 5cm (adjacent)
The hypotenuse is what we need..
[tex]cos \theta = \frac{adj}{hyp} \\ [/tex]
Substitute the given parameters
[tex]cos 60 = \frac{7}{h}\\ h =\frac{7}{cos 60}\\ h = \frac{7}{0.5}\\ h = 14in\\ [/tex]
Hence the length of the hypotenuse is 14in
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Triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1). The triangle is translated 3 units to the left and 1 unit up. What are the coordinates of B' after the translation?
a.(1, 6)
b.(–3, 6)
c.(0, 0)
d.(3, 1)
Answer:
b. [tex](-3,6)[/tex]
Step-by-step explanation:
We have been given that triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1). The triangle is translated 3 units to the left and 1 unit up.
To find the coordinates of B', we will shift x-coordinate of point B to left by 3 units and y-coordinate of point B to 1 unit up.
After the given transformation the coordinates of point B' would be:
[tex]B(0,5)\rightarrow B'((0-3),(5+1))\rightarrow (-3,6)[/tex]
Therefore, the coordinates of point B' are [tex](-3,6)[/tex] and option 'b' is the correct choice.
is -3 larger than -2?
only answer if you know and not for the points
At the beginning of an experiment, there are 600 grams of contaminants. Each hour, half of the contaminants are filtered out. How many grams of contaminants remain after 4 hours?
If f(x) = 2x - 7, what is the value of f(2)?
A.-3
B.-5
C.5
D.3
The function below can be used to calculate the cost of making a long distance call, f(m), which is based on a $2.50 initial charge and a fee of $.12 per minute, m, that the call lasts. If Natalie paid $6.82 for one call, how many minutes long was it?
What is the image of the point (4,-2) after a rotation 270 degree clockwise about the origin?
Answer:
The image of the point (4, -2) is (2, 4).
Step-by-step explanation:
Since, the rule of rotation 270 degree clockwise about the origin is,
[tex](x,y)\rightarrow (-y,x)[/tex]
Where, (-y,x) is the image of the point (x,y),
Thus, by the above rule,
[tex](4,-2)\rightarrow (-(-2), 4)[/tex]
Hence, the image of the point (4, -2) is (2, 4).
A wood frame costs $1.50. Use a property to write an equivalent expression for the cost of a wood frame.
Vonda works between 30 and 32 hours per week at a hair salon. she pays a one time $250 chair rental fee, and earns $40 per hour that she works. the hours she works are rounded to the nearest quarter hour. the function p(h)=40h−250 represents vonda's weekly pay as a function of hours worked. what is the practical domain of the function?
The practical domain of the function p(h) = 40h - 250 for Vonda's weekly pay is between 30 and 32 hours, inclusive, with increments of 0.25 hours. These values represent all the possible hours Vonda can work in a week.
To determine the practical domain of the function p(h) = 40h - 250, we need to consider the range of hours that Vonda works. The problem states that Vonda works between 30 and 32 hours per week, and her hours are rounded to the nearest quarter hour. Therefore, the possible values for h (in hours) are:
30.0030.2530.5030.7531.0031.2531.5031.7532.00Hence, the practical domain of the function p(h) is all the values between 30 and 32, inclusive, measured in quarter-hour increments.
CAN SOME ONE HELP ME WITH THIS HURRY PLEASE
HELP!!! What is the slant height x of the square pyramid? Express your answer in radical form.
To find the slant height of a square pyramid, we can use the Pythagorean theorem. The theorem should be applied as follows: A² = (y² + h²), to solve for A which is the slant height. Radical form implies that the answer will include the square root symbol.
Explanation:The question asks to find out the slant height x of a square pyramid. In order to do that, we have to invoke the Pythagorean theorem (x² + y² = h²). Here, x represents the slant height, y could be the half of the side of the base of the pyramid and h is the height from the base to the tip of the pyramid. Assuming that the pyramid is a right pyramid, the Pythagorean theorem applies.
So, the equation becomes A² = y² + h², where A is the slant height we are looking for. We solve for A to get, A = √(y² + h²). This is your slant height in radical form.
Please note you would need specific values for y and h to compute the numerical value of A.
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Where is the vertex of the parabola?
y = x2 + 6x + 7
above the x-axis
on the x-axis
on the y-axis
below the x-axis
Answer:
below the x axis
Step-by-step explanation:
i took the test
A child walks due east on the deck of a ship at 4 miles per hour.
The ship is moving north at a speed of 12 miles per hour.
Find the speed and direction of the child relative to the surface of the water.
Speed = mph
The angle of the direction from the north = (radians)
i have the speed i couldn't find the direction !,
What is the value of the missing number in the sequence below? 4, 12, 36,___, 324, 972, 2916
The missing number will be 108. The sequence is; 4, 12, 36,108, 324, 972, 2916.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
The given sequence is;
4, 12, 36,108, 324, 972, 2916
It is observed from the sequence that the following sequence follow a specific rule in which the progressive term is multiplied by a factor of 3.
[tex]\rm 4 \times 3 = 12 \\\\ 12 \times 3 = 36 \\\\ 36 \times 3 =108[/tex]
Hence, the missing number will be 108.
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Dione has 3 rolls of pennies containing 50 coins each, 4 rolls of nickels containing 40 coins each, 5 rolls of dimes containing 50 coins each, and 6 rolls of quarters containing 40 coins each. How much money does she have?
A. $106.20
B. $17.50
C. $8.00
D. $94.50
Can someone check my answer?
For y = x2 − 4x + 3,
Determine if the parabola opens up or down.
State if the vertex will be a maximum or minimum.
Find the vertex.
Find the x-intercepts.
Describe the graph of the equation.
Show all work and use complete sentences to receive full credit.,
Easy Algebra 2 Rational Expressions question
An artist drew a rectangle. the artist then modified the rectangle so thatthe length ofthe rectawngle increased by 30 percent and the width of the rectangle decreased by 40 percent. after the modification, what was the percent decrease in the area of the rectangle?
I need help with this as well
Angles X and Y are supplementary. Angle X is 3 times the measure of angle Y. What is the measure of angle X?
Answer:
The measure of ∠X is 135°
Step-by-step explanation:
Given that angles X and Y are supplementary and also angle X is 3 times the measure of angle Y.
we have to find the measure of angle X.
Since X and Y are the supplementary therefore these add up to 180° i.e
[tex]\angle X+\angle Y=180\°......(1)[/tex]
Also angle X is 3 times the measure of angle Y i.e
[tex]\angle X=3\angle Y[/tex]
Substitute this value in equation (1), we get
[tex]3\angle Y+\angle Y=180\°......(1)[/tex]
[tex]4\angle Y= 180\°[/tex]
[tex]\angle Y=\frac{180\°}{4}=45\°[/tex]
[tex]\angle X=3\times 45\°=135\° [/tex]
Hence, the measure of ∠X is 135°
What is the length of DD'?
Answer:
The length of DD' is [tex]\sqrt{29}[/tex] or 5.39 units.
Step-by-step explanation:
The distance formula is
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
From the given figure it is clear that the coordinates of D are (2,0) and coordinates of D' are (7,2).
Using distance formula we get
[tex]DD'=\sqrt{(7-2)^2+(2-0)^2}[/tex]
[tex]DD'=\sqrt{25+4}[/tex]
[tex]DD'=\sqrt{29}[/tex]
[tex]DD'\approx 5.39[/tex]
Therefore the length of DD' is [tex]\sqrt{29}[/tex] or 5.39 units.
Jana finished 1/4 of her homework at school and 2/3 of it before dinner. How much of her homework has she finished so far?
Final answer:
Jana has completed 11/12 or 11 out of 12 of her homework so far.
Explanation:
To find out how much of her homework Jana has finished so far, we need to add together the fractions of her homework completed at school and before dinner.
Jana finished 1/4 of her homework at school and 2/3 of it before dinner.
To add fractions, we need a common denominator. The least common multiple (LCM) of 4 and 3 is 12. So, we can convert both fractions to have a denominator of 12.
1/4 is equivalent to 3/12, and 2/3 is equivalent to 8/12.
Now, we can add the fractions: 3/12 + 8/12 = 11/12.
Therefore, Jana has completed 11/12 or 11 out of 12 of her homework so far.
Hey can somebody help me? I know it seems easy but I forgot the process on how to do this. Thanks in advance!
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1 1/2 - 1/2 = ???
Show your work please so I understand
Please help me, i don't understand how to do this.
Solve V = 1 3 πr2h for h.
A) 3V πr2
B) V 3πr2
C) r sqrt 3V π
D) V - 1/3 πr2